A375633 Expansion of e.g.f. exp(x^2) / (1 - x * exp(x^2/2)).

1, 1, 4, 15, 84, 555, 4440, 41265, 438480, 5240025, 69582240, 1016350335, 16194911040, 279560396115, 5197054262400, 103514720133825, 2199255573715200, 49645309340451825, 1186599954328588800, 29937224154635772975, 795051251297099596800

Offset: 0

Author

Seiichi Manyama, Aug 22 2024

Keywords

• nonn

Crossrefs

Cf. A375394, A375627.

Programs

Maple

A375633 := proc(n)
    n!*add(((n-2*k+2)/2)^k/k!,k=0..floor(n/2)) ;
end proc:
seq(A375633(n),n=0..60) ; # R. J. Mathar, Aug 23 2024

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^2)/(1-x*exp(x^2/2))))

PARI

a(n) = n!*sum(k=0, n\2, ((n-2*k+2)/2)^k/k!);

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} ((n-2*k+2)/2)^k/k!.